A recently developed Green's function and Hybrid method to analyze wave scattering problem in laminated composite plate have been employed and extended to include material damping and calculate the time domain response beyond the crack zone. Analysis has been carried out for through depth vertical crack only. Attention has been focused on plane-strain motion. Arbitrary values of damping factor have been introduced for numerical analysis to check the decaying phenomenon of the Lamb wave modes in layered composite plate. Experimental verification of the applicability of the simulation with the numerical analysis has also been carried out. It has been found that numerical analysis results are in good agreement with the experimental results.